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Instance ex6_2_6

Formatsⓘ	ams gms mod nl osil py
Primal Bounds (infeas ≤ 1e-08)ⓘ	0.00000071 p1 ( gdx sol ) (infeas: 0) -0.00000260 p2 ( gdx sol ) (infeas: 2e-14)
Other points (infeas > 1e-08)ⓘ
Dual Boundsⓘ	-0.00001850 (ANTIGONE) -0.00000260 (BARON) -0.00008993 (COUENNE) -0.00000260 (LINDO) -0.00000357 (SCIP)
Referencesⓘ	Floudas, C A, Pardalos, Panos M, Adjiman, C S, Esposito, W R, Gumus, Zeynep H, Harding, S T, Klepeis, John L, Meyer, Clifford A, and Schweiger, C A, Handbook of Test Problems in Local and Global Optimization, Kluwer Academic Publishers, 1999. McDonald, C M and Floudas, C A, Global Optimization for the Phase Stability Problem, AIChE Journal, 41:7, 1995, 1798-1814.
Sourceⓘ	Test Problem ex6.2.6 of Chapter 6 of Floudas e.a. handbook
Added to libraryⓘ	31 Jul 2001
Problem typeⓘ	NLP
#Variablesⓘ	3
#Binary Variablesⓘ	0
#Integer Variablesⓘ	0
#Nonlinear Variablesⓘ	3
#Nonlinear Binary Variablesⓘ	0
#Nonlinear Integer Variablesⓘ	0
Objective Senseⓘ	min
Objective typeⓘ	nonlinear
Objective curvatureⓘ	indefinite
#Nonzeros in Objectiveⓘ	3
#Nonlinear Nonzeros in Objectiveⓘ	3
#Constraintsⓘ	1
#Linear Constraintsⓘ	1
#Quadratic Constraintsⓘ	0
#Polynomial Constraintsⓘ	0
#Signomial Constraintsⓘ	0
#General Nonlinear Constraintsⓘ	0
Operands in Gen. Nonlin. Functionsⓘ	log mul
Constraints curvatureⓘ	linear
#Nonzeros in Jacobianⓘ	3
#Nonlinear Nonzeros in Jacobianⓘ	0
#Nonzeros in (Upper-Left) Hessian of Lagrangianⓘ	9
#Nonzeros in Diagonal of Hessian of Lagrangianⓘ	3
#Blocks in Hessian of Lagrangianⓘ	1
Minimal blocksize in Hessian of Lagrangianⓘ	3
Maximal blocksize in Hessian of Lagrangianⓘ	3
Average blocksize in Hessian of Lagrangianⓘ	3.0
#Semicontinuitiesⓘ	0
#Nonlinear Semicontinuitiesⓘ	0
#SOS type 1ⓘ	0
#SOS type 2ⓘ	0
Minimal coefficientⓘ	7.2992e-03
Maximal coefficientⓘ	4.7512e+01
Infeasibility of initial pointⓘ	0
Sparsity Jacobianⓘ
Sparsity Hessian of Lagrangianⓘ

$offlisting
*  
*  Equation counts
*      Total        E        G        L        N        X        C        B
*          2        2        0        0        0        0        0        0
*  
*  Variable counts
*                   x        b        i      s1s      s2s       sc       si
*      Total     cont   binary  integer     sos1     sos2    scont     sint
*          4        4        0        0        0        0        0        0
*  FX      0
*  
*  Nonzero counts
*      Total    const       NL      DLL
*          7        4        3        0
*
*  Solve m using NLP minimizing objvar;


Variables  objvar,x2,x3,x4;

Equations  e1,e2;


e1.. -(log(3.9235*x2 + 6.0909*x3 + 0.92*x4)*(26.9071667605344*x2 + 
     41.7710875549227*x3 + 6.30931398488382*x4) + 0.668686155614739*x2 - 
     1.14374230885457*x3 + 2.8906196099828*x4 + 9.58716676053442*log(x2)*x2 + 
     16.9310875549227*log(x3)*x3 + 0.309313984883821*log(x4)*x4 - 
     9.58716676053442*log(3.9235*x2 + 6.0909*x3 + 0.92*x4)*x2 - 
     16.9310875549227*log(3.9235*x2 + 6.0909*x3 + 0.92*x4)*x3 - 
     0.309313984883821*log(3.9235*x2 + 6.0909*x3 + 0.92*x4)*x4 + 18.32*log(x2)*
     x2 + 25.84*log(x3)*x3 + 7*log(x4)*x4 - 18.32*log(3.664*x2 + 5.168*x3 + 1.4
     *x4)*x2 - 25.84*log(3.664*x2 + 5.168*x3 + 1.4*x4)*x3 - 7*log(3.664*x2 + 
     5.168*x3 + 1.4*x4)*x4 + log(4.0643*x2 + 5.7409*x3 + 1.6741*x4)*(4.0643*x2
      + 5.7409*x3 + 1.6741*x4) + 4.0643*log(x2)*x2 + 5.7409*log(x3)*x3 + 1.6741
     *log(x4)*x4 - 4.0643*log(4.0643*x2 + 3.22644664511275*x3 + 
     1.44980651607875*x4)*x2 - 5.7409*log(5.31147575751424*x2 + 5.7409*x3 + 
     0.00729924451284409*x4)*x3 - 1.6741*log(2.25846661774355*x2 + 
     3.70876916588753*x3 + 1.6741*x4)*x4 - 30.9714667605344*log(x2)*x2 - 
     47.5119875549227*log(x3)*x3 - 7.98341398488382*log(x4)*x4) + objvar =E= 0;

e2..    x2 + x3 + x4 =E= 1;

* set non-default bounds
x2.lo = 1E-6; x2.up = 1;
x3.lo = 1E-6; x3.up = 1;
x4.lo = 1E-6; x4.up = 1;

* set non-default levels
x2.l = 0.51802;
x3.l = 0.0511;
x4.l = 0.43088;

Model m / all /;

m.limrow=0; m.limcol=0;
m.tolproj=0.0;

$if NOT '%gams.u1%' == '' $include '%gams.u1%'

$if not set NLP $set NLP NLP
Solve m using %NLP% minimizing objvar;